One way of performing image and video processing color processing is known as color gamut mapping.
A “color gamut” is a set of colors. For example, a color gamut may be the set of: colors of real objects under real illumination; colors of image(s) reproduced for display on a monitor or by film projection; synthesized colors in an animated film (e.g., CGI animation); or any other colors visible by a human or by a light capturing apparatus. In practice, color gamuts may be defined by scene illumination, real objects, image capturing devices, image reproduction devices, color spaces, standards such as NTSC, ITU-R BT rec.709 (“rec. 709”), ITU-R BT rec. 2020 (“rec. 2020”), Adobe RGB, DCI-P3, or any other present or future standards for color reproduction or any other constraint(s) on color variety.
“Color gamut mapping” is the process of mapping or redistributing colors of a source color gamut (“source colors”) to colors of a target color gamut (“target colors”). The source color gamut may be associated with any color gamut. Likewise, the target color gamut may also be associated with any color gamut. For example, a source color gamut may be associated with input image data and a target color gamut may be associated with a display device (e.g., a user device). Color gamut mapping may include changes to the saturation, hue, lightness, contrast or other aspects of colors, changes to blacks, whites or other color aspects of the source and/or target color gamut(s). For example, color gamut mapping may include tone mapping.
Color gamut mapping has important applications in the fields of image and video processing (e.g., video content production or post-production). For example, color gamut mapping is an important tool for color processing of video content (e.g., color gamut mapping may be utilized to ensure that a device's display constraints are met). Color gamut mapping may also be used to meet artistic requirements and/or as a tool by a colorist. Color gamut mapping may also be used to convert an original video into different video types for reproduction or transmission, such as for cinema, television, or the Internet. Color gamut mapping can also be used in a camera. For example, in the camera, color gamut mapping may be used to adapt a scene captured by the camera sensor to a given standard, so that the captured colors can be accurately reproduced (e.g., on a display device). The source camera gamut can be defined by the color filters of the camera sensor. Color gamut mapping might also be used in a display device to accurately display an image or video content. The target display gamut may be defined by the primary colors of the display panel. During processing, color gamut mapping may be repeated at various pixel frequencies.
Discussions of Color Gamut Mapping Include:                J. Morovic and M. R. Luo, “The Fundamentals of Gamut Mapping: A Survey”, Journal of Imaging Science and Technology, 45/3:283-290, 2001.        Montag E. D., Fairchild M. D, “Psychophysical Evaluation of Gamut Mapping Techniques Using Simple Rendered Images and Artificial Gamut Boundaries”, IEEE Trans. Image Processing, 6:977-989, 1997.        P. Zolliker, M. Dätwyler, K. Simon, On the Continuity of Gamut Mapping Algorithms, Color Imaging X: Processing, Hardcopy, and Applications. Edited by Eschbach, Reiner; Marcu, Gabriel G. Proceedings of the SPIE, Volume 5667, pp. 220-233, 2004.        
Existing color gamut mapping methods are problematic because they result in a deterioration of the consistency of colors (e.g., a deformation of the neighborhood in the resulting target color gamut) after color gamut mapping. Such problems arise from the existing methods' compression or expansion of saturation and/or of hue and/or of lightness of colors in relation to the boundaries of the source and the target color gamuts. The lightness of a color may be specified by the L coordinate of the CIELAB color space, or Lab color space, such as defined by the CIE in 1976. Similarly the lightness may also be specified by the I coordinate of the IPT color space. For example, Ebner Fritz and Mark D. Fairchild, “Development and testing of a color space (IPT) with improved hue uniformity”, Color and Imaging Conference in 1998 discusses lightness. However lightness, intensity or luminance could be used without change. The hue of a color can be obtained using psycho-physical experiments. However different viewing conditions and/or different models can lead to different hue definitions. The hue of a color might be specified by a cylindrical angle of the cylindrical coordinate representation of the color space, for example in CIELAB color space. Alternatively hue may be obtained from the color coordinates using a formula (e.g. in a RGB color space, the hue might be defined by
  hue  =            arctan      ⁡              (                                            3                        *                          (                              G                -                B                            )                                                          2              *              R                        -            G            -            B                          )              .  The boundary of a color gamut in a color space is a hull including all the colors of the color gamut.
A large part of existing color gamut mapping methods, known as cusp color gamut mapping, either compress or expand the saturation (or chroma) of colors and/or the lightness of colors in relation to a color gamut cusp. In color gamut mapping and notably in cusp color gamut mapping, non-uniform saturation modifications may occur when there is significant mismatch between primary colors defining the source color gamut and primary colors defining the target color gamut (e.g., misaligned cusp lines). Thus, the saturation gain induced by cusp color gamut mapping can be quite different for similar hues (for example for hue angle 75° the saturation gain may be 1.6 and while for hue angle 85° the saturation gain may be 1.2). This results in the problem of a degradation of the consistency of mapped colors in a color neighborhood.
Additional problems occur when a singular point (e.g. a primary or secondary color) in the cusp line of the source color gamut and the corresponding singular point in the cusp line of the target color gamut have different hues. The color neighborhood can degrade during cusp color gamut mapping when a singular point corresponds to a discontinuity of cusp line curvature. The negative impact on the color neighborhood may be even stronger if, while other conditions remain the same, the hues of corresponding singular points of the cusp lines of the source and target color gamuts, respectively, are close but not identical.
One reference that suffers from these problems is U.S. Patent Publication No. US2005/248784 to Henley et al. (“Henley”). Henley discloses a color gamut mapping method called shear mapping. The shear mapping maps in a constant-hue leaf in a color space, for example CIELAB color space, the cusp of the source gamut to the cusp of the target gamut. Henley discloses a hue rotation, which is performed as to maintain a maximum level of hue saturation. The hue rotation in Henley is a full hue rotation that maps the hue of each primary and secondary color of the input (the source color gamut) to the hue of a primary or a secondary color in the destination (the target color gamut). Full hue rotation mapping is also discussed by Green and Luo in their paper “Extending the CARISMA gamut mapping model” published at the conference Color Image Science in 2000. However, this full hue rotation results in the problem of significantly shifting hues.